A Fast Distributed Solver for Linear Systems under Generalized Diagonal Dominance

Title: A Fast Distributed Solver for Linear Systems under Generalized Diagonal Dominance
Creator: Zhang, Zhaorong; Cai, Qianqian; Fu, Minyue
Relation: IEEE Transactions on Automatic Control Vol. 66, Issue 5, p. 2423-2429
Publisher Link: http://dx.doi.org/10.1109/TAC.2020.3010261
Publisher: Institute of Electrical and Electronics Engineers (IEEE)
Resource Type: journal article
Date: 2021
Description: This article proposes a new distributed algorithm for solving linear systems associated with a sparse graph under a generalized diagonal dominance assumption. The algorithm runs iteratively on each node of the graph, with low complexities on local information exchange between neighboring nodes, local computation, and local storage. For an acyclic graph under the condition of diagonal dominance, the algorithm is shown to converge to the correct solution in a finite number of iterations, equaling the graph diameter. For a loopy graph, the algorithm is shown to converge to the correct solution asymptotically. Simulations verify that the proposed algorithm significantly outperforms the classical Jacobi method and an orthogonal projection-based method.
Subject: distributed algorithm; distributed estimation; distributed optimization; linear systems
Identifier: http://hdl.handle.net/1959.13/1475192
Identifier: uon:49477
Identifier: ISSN:0018-9286
Language: eng
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